Geometry & Topology 13 (2009) 2619–2674

DOI: 10.2140/gt.2009.13.2619

Abstract

The symplectic Floer homology HF_*(ϕ) of a symplectomorphism ϕ: Σ → Σ encodes data about the fixed points of ϕ using counts of holomorphic cylinders in R × M_ϕ, where M_ϕ is the mapping torus of ϕ. We give an algorithm to compute HF_*(ϕ) for ϕ a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel’s HF_*(h) for h any orientation-preserving mapping class.

Keywords

Floer homology, symplectomorphism, surface diffeomorphism, mapping class group, fixed point, Nielsen class

Mathematical Subject Classification

Primary: 37J10, 53D40

References

Publication

Received: 18 July 2008
Revised: 29 April 2009
Accepted: 5 February 2009
Published: 30 July 2009
Proposed: Peter Ozsváth
Seconded: Yasha Eliashberg, Leonid Polterovich

Authors